I've heard that and decided to look myself. According to their fundraising report for fiscal year 2021/22, they received $165.2m from 13m people. Removing "major gifts," $20.8m (only 18,000 people), it comes out to a bit over $11 per person. Additionally, they got $13.5m to their trust, the Wikimedia Endowment (average donation of $13.91/person). So definitely, most of their income comes from small donations.

As to whether they need it, according to their FY 21/22 financials statement, they're sitting on $198m in assets ($51m of which is cash), with an additional $52m they can't touch because they're long-term investments. However, their expenditures made up $154m. In total, they're reporting they netted $8m last year for additional assets, but assuming that everyone stopped donating, Wikipedia would probably die in a year, even with liquidation of short-term assets.

Where would you even have heard such nonsense?

How do you figure?